Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

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Mathematics : Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

The document Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev is a part of the Mathematics Course Topic-wise Tests & Solved Examples for IIT JAM Mathematics.
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Question:-1 Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Solution:
  Region bounded  by
x = 0, x = 1 and y = x, y = 1
Now we evaluate the integral by hanging the order of integral
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

Question:-2 The value of the double integral Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Solution: 
Region of integration is bounded  y=0, y = x and x = 0, x = π
 changing the order of integration
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
= 2

Question:-3 Evaluate Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Solution: 

Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

Question4:- Change the order of integration in the double integral Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Solution: 
Domain of integration is bounded  by the following curves
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
point of intersection of the curve y =2 - x2 and y = -x we get when
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
So (-1,1 ) and (2,-2 ) are the points of intersection.
Now the given integral modify by changing the order of integration we get
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Something skip follow book

 Question5:- Changing the order of integration of Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Solution: Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

The region of integration is bounded by y = 0, y = x, x = 1, x = 2 after changing the order the integration changes to
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

Question6:- Let D the trianle bounded by the y-axis the line 2y = π. Then the value of the integral Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
(a) 1/2 (b) 1 (c) 3/2 (d) 2
Solution: 

Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

Question7:- Change the order of integration in the integral Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Solution:  The domain of the double integration is bounded  by the curves y = x - 1, Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

Question8:- Let I = Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev  Then using the transformation x = rcosθ, y = rsinθ, integral is equal to
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Solution: 
Region of integration is bounded  by curves
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
for first integral,

Question9:- Evaluate integral Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
(a) 0 (b) 1/2 (c) 1 (d)2
Solution: 
Region of integration is bounded  by curves
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
 changing the order
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

Question 10:- The value of Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev equals
(a) π/4 (b) 1/2π (c) 1/4 (d) 1/2
Solution:

Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Question11:- (a) Find in the area of the smaller of the two regions enclose between Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Solution:- 

Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

Solution (b)
The region of integration is bounded  by x = 0, x = y, y = 1, y = ∞ and shown in figure changing the order
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Question12:- Let f ,Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev be a continuous function with Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Solution:  
Given, Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev be a continuous function with Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
 Now apply change of order of integration
 Domain of integration is given by graph
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

Question13:- By changing the order of integration, the integral Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev can be expressed as
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev
Solution:  
The domain of integration is bounded  y = 1, Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev  changing the order
Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

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